# Sieve

121

**sieve-maker**— …122

**sieve-plate**— …123

**Quadratic sieve**— The quadratic sieve algorithm (QS) is a modern integer factorization algorithm and, in practice, the second fastest method known (after the general number field sieve). It is still the fastest for integers under 100 decimal digits or so, and is… …124

**General number field sieve**— In number theory, the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than 100 digits. Heuristically, its complexity for factoring an integer n (consisting of log2 n bits) is of …125

**Special number field sieve**— The special number field sieve (SNFS) is a special purpose integer factorization algorithm. The general number field sieve (GNFS) was derived from it.The special number field sieve is efficient for integers of the form r e plusmn; s , where r and …126

**San Piero a Sieve**— San Piero a Sieve …127

**Legendre sieve**— In mathematics, the Legendre sieve is the simplest method in modern sieve theory. It applies the concept of the Sieve of Eratosthenes to find upper or lower bounds on the number of primes within a given set of integers. Because it is a simple… …128

**Riesel Sieve**— is a distributed computing project, running in part on the BOINC platform. Its aim is to prove that 509203 is the smallest Riesel number, by finding a prime of the form k · 2 n −1 for all odd k smaller than 509203.Progress of the projectAt the… …